Transform from a quantile format to an interval format

Internal helper function to transform from a quantile format to an interval format (which is no longer a supported forecast format, but still used internally. The function mimics an S3 generic, but is not actually an S3 generic, as we want the functions to be internal and not exported.)

Quantile format In a quantile format, a prediction is characterised by one or multiple predicted values and the corresponding quantile levels. For example, a prediction in a quantile format could be represented by the 0.05, 0.25, 0.5, 0.75 and 0.95 quantiles of the predictive distribution.

Interval format In the interval format, two quantiles are assumed to form a prediction interval. Prediction intervals need to be symmetric around the median and are characterised by a lower and an upper bound. The lower bound is defined by the lower quantile and the upper bound is defined by the upper quantile. A 90% prediction interval, for example, covers 90% of the probability mass and is defined by the 5% and 95% quantiles. A forecast could therefore be characterised by one or multiple prediction intervals, e.g. the lower and upper bounds of the 50% and 90% prediction intervals (corresponding to the 0.25 and 0.75 as well as the 0.05 and 0.095 quantiles).

Usage

quantile_to_interval(...)

quantile_to_interval_dataframe(
  forecast,
  format = "long",
  keep_quantile_col = FALSE,
  ...
)

quantile_to_interval_numeric(observed, predicted, quantile_level, ...)

Arguments

...

Arguments

forecast

A data.table with forecasts in a quantile-based format (see as_forecast_quantile()).

format

The format of the output. Either "long" or "wide". If "long" (the default), there will be a column boundary (with values either "upper" or "lower" and a column interval_range that contains the range of the interval. If "wide", there will be a column interval_range and two columns lower and upper that contain the lower and upper bounds of the prediction interval, respectively.

keep_quantile_col

keep the quantile_level column in the final output after transformation (default is FALSE). This only works if format = "long". If format = "wide", the quantile_level column will always be dropped.

observed

Numeric vector of size n with the observed values.

predicted

Numeric nxN matrix of predictive quantiles, n (number of rows) being the number of forecasts (corresponding to the number of observed values) and N (number of columns) the number of quantiles per forecast. If observed is just a single number, then predicted can just be a vector of size N.

quantile_level

Vector of of size N with the quantile levels for which predictions were made.

Value

A data.table with forecasts in an interval format.

quantile_to_interval_dataframe: a data.table in an interval format (either "long" or "wide"), with or without a quantile_level column. Rows will not be reordered.

quantile_to_interval.numeric: a data.table in a wide interval format with columns forecast_id, observed, lower, upper, and interval_range. The forecast_id column is a unique identifier for each forecast. Rows will be reordered according to forecast_id and interval_range.